Find the sum of `sum_(r=1)^n(r^n C_r)/(n C_(r-1)` .

Find the sum sum_(r=1)^n r^2(^n C_r)/(^n C_(r-1)) .

Find the sum sum_(r=0)^n^(n+r)C_r .

If sum_(r=1)^n T_r=(3^n-1), then find the sum of sum_(r=1)^n1/(T_r) .

Find the sum sum_(i=0)^r.^(n_1)C_(r-i) .^(n_2)C_i .

The value of sum_(r=1)^n(-1)^(r+1)("^n C r)/(r+1) is equal to a. -1/(n+1) b. 1/n c. 1/(n+1) d. n/(n+1)

Find the sum Sigma_(r=1)^(n) r/((r+1)!) . Also, find the sum of infinite terms.

If sum_(r=1)^n T_r=n(2n^2+9n+13), then find the sum sum_(r=1)^nsqrt(T_r)dot

Find the sum of the series sum_(r=1)^n rxxr !dot

The value of sum_(r=1)^(n+1)(sum_(k=1)^n "^k C_(r-1)) ( where r ,k ,n in N) is equal to a. 2^(n+1)-2 b. 2^(n+1)-1 c. 2^(n+1) d. none of these

Statement1: if n in Na n dn is not a multiple of 3 and (1+x+x^2)^n=sum_(r=0)^(2n)a_r x^r , then the value of sum_(r=0)^n(-1)^r a r^n C_r is zero Statement 2: The coefficient of x^n in the expansion of (1-x^3)^n is zero, if n=3k+1orn=3k+2.